Overview
Syllabus
Lattices, Post-Quantum Security, and Fully Homomorphic Encryption
Modern Cryptography
Factoring and Quantum (In)Security
Subset-Sum Problem
Subset-Sum / Knapsack • Also known as the "Knapsack" problem - Fill a knapsack of capacity b - using a selection of items of size ai.....an
Lattice/Knapsack Cryptgraphy: abridged (pre-)history . Knapsack public key cryptosystem
Subset-Sum vs Lattice Problems
Geometry of Lattices
Linear functions
Learning With Errors (LWE)
Encrypting with LWE
FHE Timeline
Homomorphic Addition
Multiplication by any constant
Public Key Encryption
How to multiply two ciphertexts
Multiplication by Encryption Nesting
Multiplication by Tensoring
Decryption is linear
Multiplication via Homomorphic Decryption
Homomorphic "decrypt and multiply"
Relation to GSW encryption
Bootstrapping and FHE
FHEW: gate bootstrapping
Summary
Additional References
Taught by
Simons Institute